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Statistically Extrapolated Nowcasting of Summertime Precipitation over the Eastern Alps


doi: 10.1007/s00376-017-6185-4

  • This paper presents a new multiple linear regression (MLR) approach to updating the hourly, extrapolated precipitation forecasts generated by the INCA (Integrated Nowcasting through Comprehensive Analysis) system for the Eastern Alps. The generalized form of the model approximates the updated precipitation forecast as a linear response to combinations of predictors selected through a backward elimination algorithm from a pool of predictors. The predictors comprise the raw output of the extrapolated precipitation forecast, the latest radar observations, the convective analysis, and the precipitation analysis. For every MLR model, bias and distribution correction procedures are designed to further correct the systematic regression errors. Applications of the MLR models to a verification dataset containing two months of qualified samples, and to one-month gridded data, are performed and evaluated. Generally, MLR yields slight, but definite, improvements in the intensity accuracy of forecasts during the late evening to morning period, and significantly improves the forecasts for large thresholds. The structure-amplitude-location scores, used to evaluate the performance of the MLR approach, based on its simulation of morphological features, indicate that MLR typically reduces the overestimation of amplitudes and generates similar horizontal structures in precipitation patterns and slightly degraded location forecasts, when compared with the extrapolated nowcasting.
    摘要: 本文基于实时雷达观测资料, 对流参数以及实时降水分析等多源数据,采用多元线性回归建立了降水外推预报的后验统计外推方法,并应用于综合分析集成临近预报系统(INCA)在阿尔卑斯山东部夏季逐小时降水外推预报,本文设计了包括偏差及分布误差在内的两步订正方法,以修正系统性回归误差,并使线性回归后的预报值概率密度分布更加接近实际的观测分布。 另外,本文对多元线性回归模型进行了交叉验证并对各项主要因子的重要性进行了讨论。采用结构-强度-位置(SAL)检验方法对2014年7月的统计外推降水预报效果进行评估后看出,统计外推预报有效地修正了传统外推易于报出过量降水的缺陷,但也易于形成较多分散小尺度降水而导致位置评分略有下降;通过个例分析可以发现,统计外推方法在局地热力对流的初始阶段能够更好地捕捉到对流单体的发展;而对线状组织对流系统,统计外推方法较原始外推预报有效地提升了降水强度预报性能。
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  • Austin G. L., A. Bellon, 1974: The use of digital weather radar records for short-term precipitation forecasting. Quart. J. Roy. Meteor. Soc., 100, 658- 664.http://onlinelibrary.wiley.com/doi/10.1002/qj.49710243123/full
    Browning K. A., C. G. Collier, 1989: Nowcasting of precipitation systems. Rev. Geophys., 27, 345- 370.http://onlinelibrary.wiley.com/doi/10.1029/RG027i003p00345/pdf
    Fox N. I., J. W. Wilson, 2005: Very short period quantitative precipitation forecasting.Atmos. Sci. Lett.6,7-11,doi: 10.1002/asl.83.http://onlinelibrary.wiley.com/doi/10.1002/asl.83/full
    Glahn H. R., D. A. Lowry, 1972: The use of model output statistics (MOS) in objective weather forecasting. J. Appl. Meteor., 11, 1203- 1211.http://adsabs.harvard.edu/abs/1972japme..11.1203g
    Golding B. W., 1998: Nimrod: A system for generating automated very short range forecasts. Meteorological Applications, 5, 1- 16.http://onlinelibrary.wiley.com/doi/10.1017/S1350482798000577/full
    Greene D. R., R. A. Clark, 1972: Vertically integrated liquid waternew analysis tool. Mon. Wea.Rev, 100, 548- 552.
    Haiden T., G. Pistotnik, 2009: Intensity-dependent parameterization of elevation effects in precipitation analysis. Advances in Geosciences, 20, 33- 38.http://www.oalib.com/paper/1367886
    Haiden T., A. Kann, C. Wittmann, G. Pistotnik, B. Bica, and C. Gruber, 2011: The integrated nowcasting through comprehensive analysis (INCA) system and its validation over the Eastern Alpine region. Wea.Forecasting, 26, 166- 183.http://adsabs.harvard.edu/abs/2011wtfor..26..166h
    Hwang Y., A. J. Clark, V. Lakshmanan, and S. E. Koch, 2015: Improved nowcasts by blending extrapolation and model forecasts. Wea.Forecasting, 30, 1201- 1217.http://adsabs.harvard.edu/abs/2015WtFor..30.1201H
    Kaltenboeck R., 2012: New generation of dual polarized weather radars in Austria. Proc. 7th European Conf. on Radar in Meteorology and Hydrology, Météo France in Toulouse, France, 25 th29 th June 2012.
    [ Available online at ]http://www.meteo.fr/cic/meetings/2012/ERAD/extended_abs/NET_166_ext_abs. pdf
    Kitzmiller D. H., S. D. Vibert, and F. G. Samplatsky, 2001: Short-range forecasts of rainfall amount from an extrapolative-statistical technique utilizing multiple remote sensor observations. Preprints Symposium on Precipitation Extremes, Albuquerque, Amer. Meteor. Soc., 266- 270.
    Lin C., S. VasiÇ A. Kilambi, B. Turner, and I. Zawadzki, 2005: Precipitation forecast skill of numerical weather prediction models and radar nowcasts. Geophys. Res. Lett., 32, L14801.http://onlinelibrary.wiley.com/doi/10.1029/2005GL023451/full
    Mand apaka, P. V., U. Germann, L. Panziera, A. Hering, 2012: Can Lagrangian extrapolation of radar fields be used for precipitation nowcasting over complex Alpine orography? Wea.Forecasting, 27, 28- 49.http://adsabs.harvard.edu/abs/2012WtFor..27...28M
    Markatou M., H. Tian, S. Biswas, and G. Hripcsak, 2005: Analysis of variance of cross-validation estimators of the generalization error. The Journal of Machine Learning Research, 6, 1127- 1168.http://dl.acm.org/citation.cfm?id=1088711
    Marshall J. S., W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor., 5, 165- 166.
    Pore N. A., W. S. Richardson, and H. P. Perrotti, 1974: Forecasting extratropical storm surges for the northeast coast of the United States. NOAA Tech. Memorandum NWS TDL-50,70 pp.
    Roberts K. J., B. A. Colle, N. Georgas, and S. B. Munch, 2015: A regression-based approach for cool-season storm surge predictions along the New York-New Jersey coast.Journal of Applied Meteorology and Climatology54,1773-1791,doi: 10.1175/JAMC-D-14-0314.1.http://adsabs.harvard.edu/abs/2015JApMC..54.1773R
    Seibert P., A. Frank, and H. Formayer, 2007: Synoptic and regional patterns of heavy precipitation in Austria.Theor. Appl. Climatol.87,139-153,doi: 10.1007/s00704-006-0198-8.http://link.springer.com/article/10.1007/s00704-006-0198-8
    Sokol Z., P. Pesice, 2012: Nowcasting of precipitation-advective statistical forecast model (SAM) for the Czech Republic. Atmospheric Research, 103, 70- 79.
    Sokol Z., D. Kitzmiller, P. Pesice, and J. Mejsnar, 2013: Comparison of precipitation nowcasting by extrapolation and statistical-advection methods. Atmospheric Research, 123, 17- 30.http://www.sciencedirect.com/science/article/pii/S0169809512003390
    Sun, J. Z., Coauthors, 2014: Use of NWP for nowcasting convective precipitation: recent progress and challenges.Bull. Amer. Meteor. Soc95,409-426,doi: 10.1175/BAMS-D-11-00263.1.http://onlinelibrary.wiley.com/resolve/reference/XREF?id=10.1175/BAMS-D-11-00263.1
    Turner B. J., I. Zawadzki, and U. Germann, 2004: Predictability of precipitation from continental radar images. Part III: Operational nowcasting implementation (MAPLE). J. Appl. Meteor., 43, 231- 248.http://adsabs.harvard.edu/abs/2004JApMe..43..231T
    Wernli H., M. Paulat, M. Hagen, and C. Frei, 2008: SAL-a novel quality measure for the verification of quantitative precipitation forecasts. Mon. Wea.Rev, 136, 4470- 4487.http://adsabs.harvard.edu/abs/2008MWRv..136.4470W
    Wilks D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed., Academic Press. 704pp.
    Wilson J. W., 2003: Thunderstorm nowcasting: Past, present and future. 31st Conference on Radar Meteorology, American Meteorological Society, 7-12Aug 2003.
    ( )https://ams.confex. com/ams/32BC31R5C/webprogram/Paper64215.html
    Wilson J. W., N. A. Crook, C. K. Mueller, J. Z. Sun, and M. Dixon, 1998: Nowcasting thunderstorms: A status report.Bull. Amer. Meteor. Soc.79,2079-2099,doi: 10.1175/1520-0477(1998) 079<2079:NTASR>2.0.CO;2.http://adsabs.harvard.edu/abs/1998BAMS...79.2079W
    Wilson J. W., Y. R. Feng, M. Chen, and R. D. Roberts, 2010: Nowcasting challenges during the Beijing Olympics: Successes, failures, and implications for future nowcasting systems. Wea.Forecasting, 25, 1691- 1714.http://adsabs.harvard.edu/abs/2010wtfor..25.1691w
    Yaqub A., P. Seibert, and H. Formayer, 2011: Diurnal precipitation cycle in Austria.Theor. Appl. Climatol.103,109-118,doi: 10.1007/s00704-010-0281-z.http://link.springer.com/article/10.1007/s00704-010-0281-z
  • [1] WANG Gaili, WONG Waikin, LIU Liping, WANG Hongyan, 2013: Application of Multi-Scale Tracking Radar Echoes Scheme in Quantitative Precipitation Nowcasting, ADVANCES IN ATMOSPHERIC SCIENCES, 30, 448-460.  doi: 10.1007/s00376-012-2026-7
    [2] Haochen LI, Chen YU, Jiangjiang XIA, Yingchun WANG, Jiang ZHU, Pingwen ZHANG, 2019: A Model Output Machine Learning Method for Grid Temperature Forecasts in the Beijing Area, ADVANCES IN ATMOSPHERIC SCIENCES, 36, 1156-1170.  doi: 10.1007/s00376-019-9023-z
    [3] FENG Yerong, WANG Ying, PENG Taoyong, YAN Jinghua, 2007: An Algorithm on Convective Weather Potential in the Early Rainy Season over the Pearl River Delta in China, ADVANCES IN ATMOSPHERIC SCIENCES, 24, 101-110.  doi: 10.1007/s00376-007-0101-2
    [4] KE Zongjian, DONG Wenjie, ZHANG Peiqun, WANG Jin, ZHAO Tianbao, 2009: An Analysis of the Difference between the Multiple Linear Regression Approach and the Multimodel Ensemble Mean, ADVANCES IN ATMOSPHERIC SCIENCES, 26, 1157-1168.  doi: 10.1007/s00376-009-8024-8
    [5] Lu YANG, Cong-Lan CHENG, Yu XIA, Min CHEN, Ming-Xuan CHEN, Han-Bin ZHANG, Xiang-Yu HUANG, 2023: Evaluation of the Added Value of Probabilistic Nowcasting Ensemble Forecasts on Regional Ensemble Forecasts, ADVANCES IN ATMOSPHERIC SCIENCES.  doi: 10.1007/s00376-022-2056-8
    [6] Qin XU, Binbin ZHOU, 2003: Retrieving Soil Water Contents from Soil Temperature Measurements by Using Linear Regression, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 849-858.  doi: 10.1007/BF02915509
    [7] Abhay SRIVASTAVA, Dongxia LIU, Chen XU, Shanfeng YUAN, Dongfang WANG, Ogunsua BABALOLA, Zhuling SUN, Zhixiong CHEN, Hongbo ZHANG, 2022: Lightning Nowcasting with an Algorithm of Thunderstorm Tracking Based on Lightning Location Data over the Beijing Area, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 178-188.  doi: 10.1007/s00376-021-0398-2
    [8] Chunlin HUANG, Hongrong SHI, Ling GAO, Mengqi LIU, Qixiang CHEN, Disong FU, Shu WANG, Yuan YUAN, Xiang′ao XIA, 2022: Fengyun-4 Geostationary Satellite-Based Solar Energy Nowcasting System and Its Application in North China, ADVANCES IN ATMOSPHERIC SCIENCES, 39, 1316-1328.  doi: 10.1007/s00376-022-1464-0
    [9] Yang LI, Yubao LIU, Rongfu SUN, Fengxia GUO, Xiaofeng XU, Haixiang XU, 2023: Convective Storm VIL and Lightning Nowcasting Using Satellite and Weather Radar Measurements Based on Multi-Task Learning Models, ADVANCES IN ATMOSPHERIC SCIENCES.  doi: 10.1007/s00376-022-2082-6
    [10] Michael B. RICHMAN, Lance M. LESLIE, Theodore B. TRAFALIS, Hicham MANSOURI, 2015: Data Selection Using Support Vector Regression, ADVANCES IN ATMOSPHERIC SCIENCES, 32, 277-286.  doi: 10.1007/s00376-014-4072-9
    [11] Lin Wantao, Ji Zhongzhen, Wang Bin, 2002: A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 699-704.  doi: 10.1007/s00376-002-0009-9
    [12] Y.L. McHall, 1993: Energetics Constraint for Linear Disturbances Development, ADVANCES IN ATMOSPHERIC SCIENCES, 10, 273-286.  doi: 10.1007/BF02658133
    [13] Li Zhijin, Ji Liren, 1994: Efficient Anomalous Forcings for Linear Problems, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 436-446.  doi: 10.1007/BF02658164
    [14] Myoung-Hwan AHN, Eun-Ha SOHN, Byong-Jun HWANG, Chu-Yong CHUNG, Xiangqian WU, 2006: Derivation of Regression Coefficients for Sea Surface Temperature Retrieval over East Asia, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 474-486.  doi: 10.1007/s00376-006-0474-7
    [15] Wang Shaobin, Song Wenzhi, Su Weihan, Zeng Jianghai, Wang Zhiping, Zhang Yuming, 1995: Nitrous Oxide Evolution from Agricultural Soil: A Regression Approach, ADVANCES IN ATMOSPHERIC SCIENCES, 12, 114-120.  doi: 10.1007/BF02661294
    [16] Keon-Tae SOHN, H. Joe KWON, Ae-Sook SUH, 2003: Prediction of Typhoon Tracks Using Dynamic Linear Models, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 379-384.  doi: 10.1007/BF02690796
    [17] Hu Yinqiao, 2002: Application of Linear Thermodynamics to the Atmospheric System. Part Ⅰ: Linear Phenomenological Relations and Thermodynamic Property of the Atmospheric System, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 448-458.  doi: 10.1007/s00376-002-0078-9
    [18] Hu Yinqiao, 2002: Application of Linear Thermodynamics to the Atmospheric System.Part Ⅱ: Exemplification of Linear Phenomenological Relations in the Atmospheric System, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 767-776.  doi: 10.1007/s00376-002-0043-7
    [19] GAO Jianyun, Tim LI, 2012: Interannual Variation of Multiple Tropical Cyclone Events in the Western North Pacific, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1279-1291.  doi: 10.1007/s00376-012-1031-1
    [20] GAO Jianyun, Tim LI, 2012: Interannual Variation of Multiple Tropical Cyclone Events in the Western North Pacific, ADVANCES IN ATMOSPHERIC SCIENCES, 29, 1279-1291.  doi: 10.1007/s00376-012-1031-1

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Manuscript received: 19 July 2016
Manuscript revised: 09 February 2017
Manuscript accepted: 28 February 2017
通讯作者: 陈斌, bchen63@163.com
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Statistically Extrapolated Nowcasting of Summertime Precipitation over the Eastern Alps

  • 1. Institute of Urban Meteorology, China Meteorological Administration, Beijing 100089, China
  • 2. Central Institute for Meteorology and Geodynamics, Vienna 1190, Austria

Abstract: This paper presents a new multiple linear regression (MLR) approach to updating the hourly, extrapolated precipitation forecasts generated by the INCA (Integrated Nowcasting through Comprehensive Analysis) system for the Eastern Alps. The generalized form of the model approximates the updated precipitation forecast as a linear response to combinations of predictors selected through a backward elimination algorithm from a pool of predictors. The predictors comprise the raw output of the extrapolated precipitation forecast, the latest radar observations, the convective analysis, and the precipitation analysis. For every MLR model, bias and distribution correction procedures are designed to further correct the systematic regression errors. Applications of the MLR models to a verification dataset containing two months of qualified samples, and to one-month gridded data, are performed and evaluated. Generally, MLR yields slight, but definite, improvements in the intensity accuracy of forecasts during the late evening to morning period, and significantly improves the forecasts for large thresholds. The structure-amplitude-location scores, used to evaluate the performance of the MLR approach, based on its simulation of morphological features, indicate that MLR typically reduces the overestimation of amplitudes and generates similar horizontal structures in precipitation patterns and slightly degraded location forecasts, when compared with the extrapolated nowcasting.

摘要: 本文基于实时雷达观测资料, 对流参数以及实时降水分析等多源数据,采用多元线性回归建立了降水外推预报的后验统计外推方法,并应用于综合分析集成临近预报系统(INCA)在阿尔卑斯山东部夏季逐小时降水外推预报,本文设计了包括偏差及分布误差在内的两步订正方法,以修正系统性回归误差,并使线性回归后的预报值概率密度分布更加接近实际的观测分布。 另外,本文对多元线性回归模型进行了交叉验证并对各项主要因子的重要性进行了讨论。采用结构-强度-位置(SAL)检验方法对2014年7月的统计外推降水预报效果进行评估后看出,统计外推预报有效地修正了传统外推易于报出过量降水的缺陷,但也易于形成较多分散小尺度降水而导致位置评分略有下降;通过个例分析可以发现,统计外推方法在局地热力对流的初始阶段能够更好地捕捉到对流单体的发展;而对线状组织对流系统,统计外推方法较原始外推预报有效地提升了降水强度预报性能。

1. Introduction
  • Rigorous demands have always been placed on the accuracy of strength, location and time for the very short-term (or nowcasting) quantitative precipitation forecasts (QPFs) that are widely used in many public service areas, including aviation, road services, construction, outdoor entertainment, agriculture, and public safety. The traditional radar-based precipitation nowcasting methods, concerned with current weather conditions and the changes over the next few tens of minutes to the ensuing 3 h, are largely based on the temporal extrapolation of trends derived from radar quantitative precipitation analysis or estimations.

    In recent years, significant achievements have been made in using numerical weather prediction (NWP) models for nowcasting applications, with the development of sophisticated assimilation of radar observations, convection-permitting NWP, and rapid updated cycling techniques (Sun et al., 2014). But, for very short-term forecasts, especially with a lead time of 1-2 h, the extrapolation methods can generally produce accurate forecasts, and the NWP results still usually have little chance to outperform (Lin et al., 2005; Wilson et al., 2010; Mandapaka et al., 2012; Hwang et al., 2015), although the accuracy reduces rapidly thereafter (Austin and Bellon, 1974; Browning and Collier, 1989; Golding, 1998). That is also an underlying reason to develop blending techniques of radar echo extrapolation with NWP, to generate a seamless 0-6-h forecast (Sun et al., 2014).

    It should also be noted that, although more organized convection systems such as squall lines and super cells can be successfully extrapolated for longer time periods (Wilson et al., 1998), the quality of extrapolation-based nowcasting for the 1-2-h lead time is not yet up to the desired level of accuracy for scales of thunderstorms and flash floods. One important reason is that the precipitation structures are often assumed persistent in a Lagrangian framework and lack the mechanistic detail required to account for the rapidly changing conditions associated with the initiation, growth and dissipation of convection systems (Fox and Wilson, 2005).

    To resolve the problem, (Mandapaka et al., 2012) mentioned that statistics will be a practical way to introduce the information about the growth and dissipation of convection systems in Meteo Swiss. (Wilks, 2011) suggested that purely statistical forecasts are useful for lead times of up to a few hours, i.e., nowcasting. However, the use of statistical methods as an alternative approach has received less attention in the nowcasting literature (Wilson, 2003), and only a few studies on nowcasting statistical applications can be found. An advective-statistical algorithm in the form of the Model Output Statistics technique (Glahn and Lowry, 1972) was developed by (Kitzmiller et al., 2001). This approach uses radar, lightning, satellite data, and NWP forecasts as predictors of a statistical regression model to forecast the probability that the maximum 3-h precipitation will exceed certain thresholds. A similar method was used by (Sokol and Pesice, 2012), which is referred to as the Statistical Advection Model, to produce 1-3-h deterministic forecasts of precipitation amounts.

    Unlike the common nowcasting systems that are based solely on a Lagrangian persistence algorithm of radar echo tracking, assuming the precipitation patterns will continue to move with a single, steady velocity derived by cross-correlating previous consecutive analyses without any growth or decay (Turner et al., 2004), INCA [Integrated Nowcasting through Comprehensive Analysis (Haiden et al., 2011)] is a system capable of providing the present analysis, nowcasting, and short-term operational QPF over the Eastern Alps, and supports a wide range of applications in multiple areas. However, the nowcasting part of the 1-h INCA precipitation forecast is produced by the phase shift based on motion vectors estimated using two or more consecutive previous analyses; and therefore, its performance in nowcasting the evolution and decay of precipitation not caused by advection, especially for thermally induced convection, needs further improvement.

    In this paper, we describe a method based on the similar framework of Statistical Advective Method—— Radar (SAMR) (Sokol et al., 2013) to find the optimal algorithms for providing improved nowcasts through integrating posterior radar observations and real-time convective analysis, with the aim to improve the 1-h precipitation extrapolation nowcasting performance of the INCA system over the Eastern Alps during the summer season. Within the current operational implementation at ZAMG, every INCA 1-h precipitation nowcast beginning at T UTC finishes almost simultaneously, with the radar volume scanning beginning at T+10 min (T+0.16 h). Therefore, an instant, "posterior" correction of the 1-h precipitation nowcast is possible using the latest two radar volume scans valid at T+5 min and T+10 min, assuming a further improvement of the 1-h precipitation nowcast valid from [T, T+1 h] with the latest information about the onset, duration, and intensity of convections introduced. Furthermore, not only could the real-time radar products be included as predictors, but the latest convective diagnostic analysis, including the convective available potential energy (CAPE) and convection inhibition index (CIN), valid at T UTC, could also be regarded as candidate predictors, with the goal of incorporating more information regarding the convective potential within the nowcasting period.

    The remainder of this paper is organized into four parts. The operational INCA system and its nowcasting module are briefly described in section 2. The development of the instant posterior statistical model is presented in more detail in section 3. In section 4, cross validation, significance of different predictors, applications and evaluation results are discussed. The results from pre-implementation tests using independent datasets, including verification scores and case studies, are also examined. Finally, our conclusions are presented in section 5.

2. INCA precipitation nowcasting
  • The INCA system is a multi-parameter analysis and nowcasting tool that has been in operational use at ZAMG for almost a decade, and is under continuous development (Haiden et al., 2011). The INCA precipitation module consists of the following three parts: analysis, nowcasting, and blending with an NWP model. For the analysis part, INCA computes a weighted combination of rain gauge and radar data, taking the reduced visibility of radar in mountainous areas into account. The elevation dependence of precipitation is also considered by applying the parameterization described in (Haiden and Pistotnik, 2009). The nowcasting range is 6 h. In the first 2 h, the precipitation fields are predicted by an extrapolation based on Lagrangian persistence. From T+2 h to T+6 h, the nowcast fields are smoothly merged with an NWP model such that, for lead times greater than 6 h, INCA essentially provides downscaled NWP information, or a combination of different NWP models. In the operational setting used at ZAMG, a weighted combination of the ECMWF and ALARO5 (the operational limited area model) models are used for the forecast. INCA runs on a regular 1 km × 1 km domain that covers Austria and parts of neighboring countries (see Fig. 1). The temporal resolution and update frequency are both 15 min. INCA analysis and forecast fields are provided in near real-time, with only a few minutes' computation time.

    Figure 1.  Topography (unit: m) and the locations (triangles) of the five operational C-band weather radar sites that constitute the Austrian radar network (the data from the radar displayed as the white triangle are unavailable in this study). The entire INCA domain, with 700× 400 1-km2 grid cells, is decomposed into 2800 small-scale patches of 10× 10 grid points. The center of each small patch is marked with a black +.

    The radar dataset used in this study is a composite of data from the Austrian radar network, which consists of five C-band weather radars (see Fig. 1) operated by Austro Control (Kaltenboeck, 2012). Ground clutter has been removed from the data using Doppler processing and multi-temporal/multi-parameter statistical filters. A series of radar-derived products are provided with a temporal resolution of 5 min, and these products will be described in more detail in section 3.

3. Development of statistical models
  • In this study, a multiple linear regression (MLR) approach, which is both robust and easily applicable, is used to estimate the relations between predictors and predictands. MLR seeks to summarize the linear relationship between the predictand and multiple predictor variables and is ultimately expressed as a linear combination of K predictors that can generate the least error for the prediction of \(\hat{y}\) given observations of each predictor xi from the training dataset, as follows: \begin{equation} \hat{y}=\beta_0+\sum_{i=1}^K\beta_i x_i \ \ (1)\end{equation} where βi is the coefficient determined by the regression. The MLR models are developed independently for 1-h INCA precipitation forecasts initiating from 0000, 0100, …., 2300 UTC, respectively.

    Screening the regression, i.e., selecting a high-quality set of predictors from a pool of potential predictors to avoid the problem of over-fitting and to remove redundant predictors, is an important step in the statistical prediction procedure (Wilks, 2011). In this study, the predictors are selected using backward elimination (Wilks, 2011), and the relative importance of the selected predictors is discussed in section 4.

  • Assuming that the initial time of each MLR forecast model is valid at t=T UTC, the candidate predictors are provided from the four following sources:

    (1) QPF: INCA hourly operational extrapolation precipitation forecast itself, valid at time T+1 h UTC (i.e., the forecast accumulated precipitation from [T, T+1 h] UTC), which is based on the Lagrangian persistence.

    (2) The radar products [(i)-(iii) below]: products derived from composite measurements of five C-band (5.33 cm) radars covering the INCA domain valid at [T+0.16 h] UTC.

    (i) MAXCAPPI: Analysis of the maximum constant-altitude plan position indicator above sea level. A CAPPI (constant altitude plan position indicator) and a MAXCAPPI (maximum CAPPI) product are provided every 5 min on a Cartesian grid with a spatial resolution of 1 km. Both products are reduced to 14 reflectivity classes ("no rain", 11.8, 14.0, 19.5, 22.0, 26.7, 30.0, 34.2, 38.0, 41.8, 46.0, 50.2, 54.3, and 58.0 dBZ). The MAXCAPPI product in combination with the Marshall-Palmer relationship is Z=200 r1.6 (Marshall and Palmer, 1948) and is used for the estimation of precipitation, where Z is the sum of six powers of drop diameters in unit volume, and r is the rate of rainfall.

    (ii) VIL: Vertically integrated liquid water content. This product can be used as a measure of severe weather potential, such as an indicator of the size of prospective hail and the potential amount of rain during a thunderstorm (Greene and Clark, 1972). It is derived from the CAPPI product by integrating the liquid water content calculated from reflectivity within a vertical column.

    (iii) ECHOTOP: The radar echo top defined as the maximum height where a reflectivity of at least 4 dBZ is recorded. It is an estimate of the top of an area of precipitation that gives an impression of the intensity of updrafts. The vertical resolution of ECHOTOP in this study is limited to 1 km by the resolution of the CAPPI data.

    (3) The INCA convective parameter analysis valid at time T UTC, including (i) the CAPE, (ii) the CIN, and (iii) the moisture convergence (MCONV). The areas with positive MCONV values (convergence of moisture flux) indicate the potential for convective forcing, whereas negative values indicate divergence on the ground and thus subsidence in the air mass above.

    (4) QPE: The INCA hourly operational precipitation analysis valid at time T UTC; i.e., the analyzed accumulated precipitation from [T-1, T] UTC acquired from the combination of radar, rain gauge information, and the inclusion of a parameterization of elevation effects in mountain areas. This analysis comprises the precipitation truth 1 h ahead of the current forecast time. This predictor represents the possible correlation of persistent precipitation between the two consecutive time periods of [T-1, T] UTC and [T, T+1] UTC.

    The list of predictor variables is given in Table 1, and the generalized form of Eq. (1) can be rewritten as Eq. (2), with all potential predictors and β representing the model coefficients (Table 1): \begin{eqnarray} {\rm QPF}(T+1)&=&\beta_0+\beta_1{\rm QPF}(T+1)+\beta_2{\rm QPE}(T)+\nonumber\\ &&\beta_3{\rm MCAPPI}(T+0.16)+\beta_4{\rm VIL}(T+0.16)+\nonumber\\ &&\beta_5{\rm ECHOTOP}(T+0.16)+\beta_6{\rm CAPE}(T)+\nonumber\\ &&\beta_7{\rm CIN}(T)+\beta_8{\rm MCONV}(T) \ \ (2)\end{eqnarray}

  • In this paper, the historical radar composite products, INCA analysis and forecasts, which are available every 5 and 15 min, are from three summer seasons (June to September) over the period 2012-14. For every MLR model constructed for each initiating forecast hour, the total 12-month dataset is divided into the following two parts: the training dataset and verification dataset. The training part contains 10 randomly selected months of data from which the regression equations are derived. The remaining two months, August 2013 and July 2014, make up the verification part, which will be used to validate the forecast performance of the MLR.

    In this study, on a grid point basis, the number of qualified precipitation events is still limited in order to be statistically significant. Therefore, an alternative method to construct a sample dataset and derive a regression model for a cluster of N× N grid points has been applied. Here, we set N as 10, as this value is large enough to ensure that the samples collected grid-by-grid may reach a significant value, but small enough to be representative of the local orographic and precipitation features. Therefore, the entire INCA domain with 700× 400 1-km2 grid cells is decomposed into 2800 small-scale patches of 10× 10 grid points (Fig. 1). For every patch domain, a common sample dataset is constructed by collecting qualified samples ( QPF>0) from each of the 100 grid points; and thereafter, a common MLR equation is then derived using the dataset, and will be assigned to all points within the domain. Overall, the sample size of the training dataset for each patch domain is approximately 5000-10 000.

    The 2800 small patches are traversed to calculate regression coefficients and perform a backward elimination of predictors and statistical output correction. For the predictors that fail to pass the backward elimination, their corresponding coefficients will be set to 0.

  • There are two different types of bias that need to be considered. The first is the systematic bias usually shown from the regression models derived from the various fitting approaches (Roberts et al., 2015). The important source of bias in MLR nowcasts is from the nonlinear nature of precipitation. Therefore, both incomplete thermodynamic processes and the linear approximation of the regression may contribute to systematic errors in forecasts of the MLR models. Second, because the phenomena that an MLR can linearly describe are the characteristics of samples that concentrate near the climatological mean of the training dataset, the behavior of the MLR mostly depends on the probability of the predictand in the training dataset. The precipitation record samples with less probability, such as the observed large-amount precipitation events, would be treated as outliers, although they are correct. Regression often has difficulty replicating the occurrence of extremes as frequently as they are observed (Roberts et al., 2015); therefore, it is also important to ensure that the predicted precipitation has the correct relative frequency of amounts.

    Figure 2.  Scatterplots of observed and fitted values of precipitation from the training dataset, including (a) without correction, (b) with bias correction, and (c) with bias and distribution correction. Also shown are the probability density histograms of (d) observed precipitation, (e) fitted values without correction, (f) fitted values with bias and distribution correction, (g) fitted values without correction minus observed precipitation, (h) fitted values with bias correction minus observed precipitation, and (i) fitted values with bias and distribution correction minus observed precipitation. The red line serves as the 1:1 reference line. The black line is the line of best fit.

    In this study, the direct output from the application of the MLR models to the training dataset reveals that statistical models usually tend to overpredict small amounts of precipitation but underpredict large amounts. As illustrated in Fig. 2a, the direct outputs of the MLR models tend to systematically underpredict the moderate to strong precipitation events with intensities greater than 4 mm h-1. Also, a large portion of 2-4 mm h-1 precipitation is also underpredicted to 0-2 mm h-1 while overpredicting weak precipitation events below 1 mm h-1. Consequently, MLR overpredicts the frequencies of the observed precipitation amount intervals between 1 and 2 mm h-1 but underpredicts those below 1 mm h-1, which leads to a distorted probability distribution of the MLR fitted values (Fig. 2e) compared with observations (Fig. 2d) and significantly non-Gaussian forecast errors (Fig. 2g). To resolve the above two deficiencies, both bias and distribution corrections need to be performed.

    To measure the goodness-of-fit of a regression, the coefficient of determination, R2, can be computed from \begin{equation} R^2=\dfrac{\sum(\hat{y}-\bar{y})^2}{\sum(y-\bar{y})^2}=1-\dfrac{\sum r^2}{\sum(y-\bar{y})^2} , (3)\end{equation} where y, \(\hat{y}\) and \(\bar{y}\) are the predictand, regression prediction and the mean of the predictand, respectively; and r2 is the residual. R2 is the proportion of the variation of the predictand that is described or accounted for by the regression. If no effective regression can be reached, R2 is equal to 0, while for a perfect regression R2 is equal to 1. In this way, R2 can be used as an index to evaluate the quality of a linear regression and quantify the nature and strength of the linear relationship between the predictand and predictors (Wilks, 2011).

    (Pore et al., 1974) and (Roberts et al., 2015) described a bias correction approach by multiplying the MLR predictions by the reciprocal of the multiple correlation coefficients, or \(1/\sqrt{R^2}\), which is also equivalent to the square root of the coefficient of determination defined as Eq. (3). An identical approach is used in this study. As shown in Fig. 2b, the bias-corrected output of the MLR is generally pushed towards the direction with larger fitted values. In this way, the underprediction for moderate observations is partly corrected, but with the sacrifice of a higher overprediction for minor precipitation, which leads to the non-Gaussian distribution with a higher frequency of positive forecast errors (Fig. 2h).

    Distribution correction is performed after bias correction by compulsorily constructing the distribution of the output of the MLRs to be close to that of the corresponding predictand (Sokol and Pesice, 2012). First, for the observed predictand Ok,k=1,…,M and its direct MLR forecasted counterpart yk, out,k=1,…,M from the training dataset, their percentile values of 0.01,1,2,…,99, and 99.9, denoted as Oi,i=1,…,101 and Yi,i=1,…,101, can be obtained and archived as look-up tables for each MLR equation. The modified value yk, mod,k=1,…,M can be calculated using linear interpolation as follows: \begin{equation} y_{k,{\rm mod}}=O_i+\dfrac{y_{k,{\rm out}}-Y_i}{Y_{i+1}-Y_i}(O_{i+1}-O_i) , \ \ (4)\end{equation} where Yi≤ yk, out≤ Yi+1, O0=0 and O102=100 mm are set to ensure that for any yk, out, the corresponding Oi and Oi+1 exist.

    After applying the two-step corrections, the probability frequency distribution of forecast values (Fig. 2f) looks similar to those of the observations, and the distributions of the forecast errors are closer to Gaussian (Fig. 2i). It should be noted that some slight negative forecasted values generated by the statistical models (Fig. 2a), which partly contribute to the distortion of probability frequency (Fig. 2e), are also corrected after the distribution correction taken. This result demonstrates that the correction procedures will significantly improve the quality and distribution of the model outputs.

  • The MLR models are developed for the predictand (T+1 h precipitation), initiating every hour at 0000, 0100, …, 2300 UTC. With the entire domain decomposed into square patches with N× N grid points (N=10 in this study), the MLR models are constructed using the training dataset for each patch domain as follows:

    (1) MLR regression equations are derived and optimized using a backward elimination technique.

    (2) For each patch domain, the MLR regression coefficients are updated by multiplying by the reciprocal of the multiple correlation coefficients for bias correction, and the look-up tables containing the percentile values of the predictand Oi and fitted values Yi of the MLR model are then obtained for distribution correction.

    (3) The identical configuration of the regression coefficients and its corresponding percentile look-up table are shared with all grid points inside the current patch domain.

    (4) Regression coefficients βi, i=0,1,…,K in Eq. (1) of every grid point of the entire domain are then assigned, with all patch domains traversed.

    In an operational environment, the implementation of the MLR model must fit the operation of the INCA system and the radar data update frequency. Assuming the current time is [T+0.16 h] UTC, the predictors that can be obtained are as follows: (i) the latest radar products valid at [T+0.16 h] UTC; (ii) a 1-h precipitation analysis valid at T UTC (with precipitation from [T-1 h, T] UTC); (iii) a 1-h extrapolated precipitation forecast valid at T+1 h UTC; and (iv) convective analysis fields from T UTC. With the above data, the prepared MLR models will be implemented using the following steps:

    (1) Calculation of predictor values and forecasts with the MLR models.

    (2) Bias and distribution correction of the updated forecasts of the MLR with the look-up tables from Eq. (4).

    The above implementation procedure can be completed within 1 min. Therefore, the updated T+1 h precipitation forecasts made by the MLR models can be issued with only a very short delay.

4. Results and discussion
  • The robustness of all MLR models is tested by performing a cross-validation analysis, which simulates predictions for the future using unknown data by repeating the fitting procedure on data subsets and then examining the predictions on the data portions left out of each of these subsets (Wilks, 2011). If the deterioration in forecast precision (e.g., the unavoidable increase in mean squared error) is judged to be acceptable, the equation can be regarded as robust.

    In this paper, for all MLR models at 0000, 0100, …, 2300 UTC, we perform a 10-fold cross-validation (Markatou et al., 2005), in which a random holdout of 10% of the training dataset is used for validation and the non-overlapping remaining 90% of the data are used to train the models with the fixed predictors of the MLR model. This procedure is performed repeatedly, 10 times in total, until all available data have been used as the training and validation subset once. We use the R2 shrinkage (dR2=R2| MLR-R2| CV) and RMSE inflation [d RMSE=( RMSE| MLR- RMSE| CV)/( RMSE| MLR)× 100%], where the subscripts of MLR and CV represent MLR and the cross-validation, respectively, to quantitatively measure the performance difference between the MLR model and its cross-validation results. The MLR model is more stable as dR2 and d RMSE get closer to zero.

    Figure 3.  Box plots of R2 shrinkage and RMSE inflation for MLR models at 0000,0100,…,2300 UTC.

    Figure 3 illustrates the box-and-whisker plots of dR2 and d RMSE for the MLR models of every hour at 0000, 0100, …, 2300 UTC. The most significant differences of R2 and RMSE between MLR and its cross-validation occur in the afternoon, corresponding to the active convection period, whereas the changes are minor, as even the largest amplitude of R2 shrinkage is less than 0.01, and the RMSE inflation does not exceed 0.8%. From the cross-validation results, the overall robustness of the MLR models can be considered satisfactory and worth testing in future operational implementation.

  • The optimized combination of predictors for every MLR model on every patch domain and lead time is obtained from the screening algorithm of backward elimination. For most MLR models, not all potential predictors pass the screening procedure, and the most commonly selected predictors are those directly related to the precipitation amount, i.e., the extrapolated precipitation forecast (QPF), MAXCAPPI, and the precipitation analysis at the initial time (QPE).

    To identify the relative importance of each predictor, all MLR models are reconstructed with the standardized samples simply by subtracting the sample mean of the training dataset and dividing by the corresponding sample standard deviation. In this way, the derived normalized linear regression coefficients directly indicate the relative importance of each predictor (Wilks, 2011).

    Figure 4.  Distributions of the normalized linear regression coefficients for CAPE, CIN, MAXMCAPPI, QPE, and QPF at 0100 UTC (left) and 1300 UTC (right).

    Figure 4 shows the distributions of the normalized linear regression coefficients of the most commonly selected predictors for 0100 and 1300 UTC, corresponding to local nighttime and afternoon, respectively. The diurnal cycle and geographic characteristics related to convective precipitation can be identified over the Eastern Alps as well. Obviously, QPF is the most important and even the predominant predictor, especially in the area beyond radar coverage and at night. MAXCAPPI is the predictor with the second highest importance, especially during the afternoon, and is almost as significant as QPF itself within the radar coverage area; however, at 0100 UTC, it is much less important than at 1300 UTC in the mountainous area of western Austria. For QPE, the 1-h accumulated precipitation valid at the initial time, its positive coefficients are significant on the northern slopes of the Eastern Alps, revealing that precipitation occurring in this region is more persistent and non-convective, which is consistent with the conclusion that the orographic effects of the Alps may enhance the precipitation advected from westerly and northwesterly directions (Seibert et al., 2007; Yaqub et al., 2011). The distributions of convective-parameter predictors, such as CAPE and CIN, also correspond well with the isolated distribution of the negative values of the QPE coefficients, especially over northern Italy and the eastern part of the domain, implying the orographic and thermally induced convection driven by the southerly flows brings humidity from the Mediterranean (Yaqub et al., 2011).

  • The MLR models used to predict precipitation initialized at 0000, 0100, 0200, …, 2300 UTC with a 1-h lead time are first applied to the verification dataset that comprises the two months of sample data from August 2013 and July 2014. The experiments INCAOP and INCAMLR represent the original operational QPF nowcasting from INCA and the MLR predicted counterpart, i.e., the QPF and predicted QPF in Eq. (2).

    Figure 5.  Evaluation of the hourly precipitation forecasts by INCAMLR and INCAOP using the verification dataset: (a) RMSE; (b) absolute error; (c) bias; (d) correlation coefficient; (e) CSI; and (f) BS scores.

    Since the verification dataset comprises samples collected from discrete grid points, the forecasts from INCAOP and INCAMLR are evaluated using standard measures, including root-mean-square error (RMSE), mean absolute error (MAE), bias error (BIAS), correlation coefficient (CC), critical success index (CSI), and bias score (BS), in terms of the contingency table. The scores from INCAOP and INCAMLR display diurnal variations, with maximum and minimum values at 1500 and 0500 UTC, respectively. INCAMLR has lower quantitative errors, as described by the RMSE and MAE, which is more obvious for forecasts initiated during the local afternoon to early evening between 1200 and 1700 UTC. There is a slight but definite improvement during the late evening to morning between 0300 and 0800 UTC. INCAMLR also has BIAS values much closer to 1, i.e., the amount of overprediction of the extrapolated precipitation forecasts is significantly reduced in the MLR forecasts over the entire 24-h period.

    The CSI and BS scores are calculated for thresholds of 1, 5, and 10 mm h-1. For 1 mm h-1, the CSI scores of INCAMLR generally degrade slightly, and this result can be attributed in part to the slight area overprediction yielded by INCAMLR with the slightly larger BS values. However, the BS scores of INCAMLR for 5 and 10 mm h-1 reduce significantly to approximately 1 when combined with comparable and larger CSI scores throughout the majority of the 24-h period, which indicates that the MLR approach leads to better performance with a more reasonable distribution and more reasonable amounts for higher thresholds (Fig. 5).

    Figure 6.  Evaluation of hourly precipitation forecasts by INCAMLR and INCAOP for the period of 1-31 July 2014: (a) CSI and (b) BS scores for T+1 h.

    The prevailing precipitation type probably accounts for the diurnal cycle of the evaluation scores. Precipitation occurring at night and in the early morning is less convective and more persistent than daytime rainfall, which is the favorable type for extrapolation to predict, and extrapolation itself is the dominant predictor. Moreover, for the active convection period, such as the afternoon and early evening, QPF is a less important predictor, but other radar and convection predictors introduce more statistically acquired information about the evolution of convection, which leads to both better amounts and a more realistic spatial distribution of the precipitation forecast.

  • The second application of the MLR models is a 1-month experiment with all predictors prepared within the entire domain, rather than from qualified samples on grid points that meet certain screening criteria, as for the verification dataset. July 2014 represents a typical month characterized by active convection and is selected for further implementation and detailed evaluation. The implementation of the MLR statistical models is performed hourly with all gridded predictors. In addition to the classical point-verification measures outlined above, the object-oriented spatial verification and structure-amplitude-location (SAL) (Wernli et al., 2008) methods are applied for further evaluation and comparison of INCAOP and INCAMLR. In a pre-specified region of interest where the SAL scores are evaluated, objects are identified as coherent areas of grid points in the observed and predicted precipitation fields with precipitation amounts greater or equal to a given threshold. The structure score S describes the quality of the forecasted size and shape of the precipitation and varies from -2 to 2, indicating the predicted precipitation from too small/peaked to large/flat. The amplitude score A corresponds to the normalized difference of the domain-averaged precipitation values of the model and the observations. Its quantity varies between -2 and 2, with values of -2 and 2 indicating underpredicted and overpredicted total precipitation amounts, respectively. The location score L quantifies whether the predicted precipitation objects are situated at the correct location, and it ranges from 0 to 2, measuring whether the precipitation objects are predicted at the correct position or not. For all three scores (i.e., S, A and L), a perfect forecast would yield values of zero. The operational precipitation analysis from INCA is provided as the gridded "truth" against which all evaluations are performed.

    The verification scores of the INCAMLR and INCAOP forecasts and their comparison by CSI and BS are shown in Fig. 6 for the T+1 h forecasts from every hour. Generally, the comparison of the diurnal variations of INCAMLR and INCAOP performances for the three thresholds show less variability than the results from the verification dataset. From the SAL scores, it is found that the location score shows a similar diurnal variation for both experiments and for most of the analysis period (Fig. 7), and the amplitude score of INCAMLR is closer to 0, indicating that the regression model reduces the overestimation of INCAOP, which is consistent with the verification results from the CSI/BS combination scores. However, the larger negative structure score reveals that INCAMLR degrades the distribution forecast performance. A similar impression can be acquired by subjective comparison, as INCAMLR may yield more scattered or discontinuous small-scale precipitation due to the correction procedure after the regression forecast.

    Figure 7.  SAL evaluation of 0-1-h hourly precipitation forecasts by INCAMLR and INCAOP for the period 1-31 July 2014.

  • Two types of convection cases, locally initiated and a squall line, are selected to further demonstrate the effects of the application of the regression model. Generally, there are no substantial differences between the two experiments, but evident improvements can still be identified in the structure and strength of the precipitation forecasts; and in particular, the more detailed small-scale structures of scattering cells are supplemented by the incorporation of the latest radar and convection information. For the local convection case, INCAMLR is able to capture more scattering convective cells at the initiation stage than INCAOP, e.g., 1100 and 1400 UTC 7 July 2014 (Fig. 8). For the squall line case that occurred between 1600 and 2100 UTC 16 July 2014 (Fig. 9), the line-organized structure is reproduced almost as well as in INCAOP, but the strength of the convection in some areas is modified to become closer to the truth. This result demonstrates that INCAMLR tends to smooth out the large precipitation centers predicted by INCAOP, and these results explain why INCAMLR yields BIAS values much closer to 1 and lower RMSE scores, since it is more sensitive to large outliers.

    Figure 8.  Time series of T+1 precipitation forecasts by INCAOP (left) and INCAMLR (middle). The right-hand column shows the corresponding precipitation analysis, valid from 1100 to 1400 UTC 7 July 2014 (Unit: mm h-1).

    Figure 9.  Time series of 0-1-h precipitation forecasts by INCAOP (left) and INCAMLR (middle). The right-hand column is the corresponding precipitation analysis, valid from 1600 to 2100 UTC 11 July 2014 (Unit: mm h-1).

5. Conclusions
  • This paper describes an MLR approach used to update the hourly nowcasting extrapolated precipitation forecast from the INCA system over the Eastern Alps. The method approximates the updated precipitation forecast as a linear response to combinations of predictors selected through a backward elimination algorithm from a pool of potential predictors comprising the raw output of the extrapolated precipitation forecast, the posterior radar observations, the latest convective diagnostic analyses, and the precipitation analysis. For every MLR model, bias and distribution correction steps are taken to further correct the systematic regression errors. The bias correction is achieved by multiplying the MLR coefficients by the reciprocal of the multiple correlation coefficients. To ensure that the MLR behavior follows the climatological probability density distribution, look-up tables containing percentile values of the predictand Oi and fitted values Yi of the MLR models are obtained and are used for further distribution correction of the regression output.

    The significance of the different predictors is also discussed. The diurnal cycle and geographic characteristics of the normalized linear regression coefficients reveal that the extrapolated precipitation forecast itself is the most important, and even the predominant predictor, especially in areas that are outside radar coverage. MAXCAPPI is almost as significant as QPF in areas with radar coverage. For the predictor QPE to be valid at the initial time, its coefficients are more significant during nighttime because precipitation at that time is more persistent and of non-convective character than daytime precipitation, and vice versa in the case of convection-related predictors.

    The MLR approach is applied to the verification dataset containing two months of qualified samples, and in one-month gridded data; the results are then evaluated. The following conclusions are drawn:

    (1) Compared with the extrapolated results, MLR yields lower quantitative errors (as described by the RMSE and MAE). Slight, but definite improvements can be identified between late evening and morning. The BIAS values of INCAMLR are much closer to 1, i.e., the amount of overprediction in the extrapolated precipitation forecasts is reduced slightly by using the MLR forecasts throughout the 24-h forecast period.

    (2) The category scores of CSI and BS combinations reveal that, in general, INCAMLR slightly degrades the performance of INCAOP for small amounts of precipitation (<1 mm h-1). However, the improvements for large-threshold precipitation (e.g., 5 and 10 mm h-1) are more pronounced, especially during the daytime. The SAL scores, used to evaluate the morphological features, indicate that INCAMLR mostly reduces the amplitude of the overestimation of INCAOP and shows similar location scores. However, the larger negative structure score reveals that INCAMLR deteriorates the spatial distribution of the precipitation slightly.

    (3) Two different types of convection cases are presented for further discussion. Our subjective comparison indicates that, for local convection, INCAMLR is able to capture more scattering convective cells at the initiation stage than INCAOP, and does not affect the structure forecast by INCAOP. The strong precipitation centers in some areas are smoothed and modified and, for most of the time, INCAMLR has the more accurate results when compared with observations.

    The MLR method can be applied as the final correction step before the extrapolated precipitation products are released to nowcasting end-users. However, some issues for future implementation in an operational environment still need to be addressed. First, the MLR models can be only applied at grid points meeting the condition of QPF >1, to avoid its negative impact on the performance for small amounts of precipitation (<1 mm h-1). As shown in Figs. 8 and 9, some "mosaics" can be identified from the MLR precipitation forecasts due to the discontinuous predictions generated from different MLR models of neighboring domains. A blurring/smoothing method needs to be developed, and hopefully the problem will be finally resolved, with the MLR models constructed point-by-point, in the future. Finally, it is important to closely synchronize the operation of INCA and radar nowcasting systems to effectively use the latest available data.

    It is important to note that, although these results are promising, uncertainties remain because of the limited sample size. Experiments using various combinations of training and verification data will be carried out in the future if sufficiently large training samples can be used to develop the MLR models. In addition, according to the results of regression quality control, linear models cannot always explain a large proportion of the variance in the observations from the training datasets; therefore, the possibility of incorporating additional nonlinear thermodynamic predictors with a more sophisticated statistical technique (e.g., neural networks or a nonlinear regression model) is worthy of consideration. More data sources, e.g., convection-resolving NWP forecasts or satellite data, especially for the initiation of cells before precipitation begins, will also be considered as potential predictors for statistical models to benefit the nowcasting of the initiation and decay of convective precipitation in the future. Finally, a comparison of such a statistical model with a convection-resolving NWP (e.g., the High-Resolution Rapid Refresh (HRRR)) will be very interesting in the medium-term future.

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